Rigidity of bounded type cubic Siegel polynomials
Dynamical Systems
2024-08-02 v2
Abstract
We prove that if two non-renormalizable cubic Siegel polynomials with bounded type rotation numbers are combinatorially equivalent, then they are also conformally equivalent. As a consequence, we show that in the one-parameter slice of cubic Siegel polynomials considered by Zakeri [Za2], the locus of non-renormalizable maps is homeomorphic to a double-copy of a quadratic Siegel filled Julia set (minus the Siegel disk) glued along the Siegel boundary. This verifies the the conjecture of Blokh-Oversteegen-Ptacek-Timorin [BlOvPtTi] for bounded type rotation numbers.
Cite
@article{arxiv.2311.00431,
title = {Rigidity of bounded type cubic Siegel polynomials},
author = {Jonguk Yang and Runze Zhang},
journal= {arXiv preprint arXiv:2311.00431},
year = {2024}
}